Gaussian Definition and 706 Threads

Homework Statement I am asked to solve this question using pivoting technique ... so , in I , I switched the R1 and R2 so that a11 is max , in III , i switched R9 nad R10 , so that a22 is max . But , in IV , i found that the a31 become -2/9 , which is not 0 anymore , what's wrong with my...

Homework Statement Homework EquationsThe Attempt at a Solution Okay, parts a-c are zero as they are within both shells. Lets begin with d because i fear I am just repeating the same error in all of the following parts. Part d qenclosed=ρ(4πr^3/3-4πa^3/3) =...

Homework Statement A metal sphere of radius a is surrounded by a metal shell of inner radius b and outer radius R, as shown in the diagram below. The flux through a spherical Gaussian surface located between a and b is 1.20Q/εo and the flux through a spherical Gaussian surface just outside R is...

Homework Statement An electric field given by https://edugen.wileyplus.com/edugen/shared/assignment/test/session.quest2560893entrance1_N10030.mml?size=14&ver=1486488694211 =...

Homework Statement Homework Equations σ=q/(4πr^2)→q=σ(4πr^2) E=q/(4πEod^2) E=(4πr^2σ)/(4πEod^2)The Attempt at a Solution So the first thing that i could include was that the point p was inside Shell 1 and therefor would not be affected by Shell 1. So it should be a fairly simple plug in the...

I have been exploring the paper: Statistical Tests for the Gaussian Nature of Primordial Fluctuations Through CBR Experiments http://lss.fnal.gov/archive/1993/pub/Pub-93-294-A.pdf . Here is a quote. Cosmic inflation [1], on one hand, provides a natural way to generate Gaussian initial...

Homework Statement Hi, I am trying to follow my book's hint that to find the normalization factor one should "Diagnoalize ##\Sigma^{-1}## to get ##n## Gaussian which will have variance given by the eigenvalues of ##\Sigma## . Then integrate gives ##\sqrt{2\pi}\Lambda_i##, then use that the...

Hello, guys. I am trying to solve for characteristic function of normal distribution and I've got to the point where some manipulation has been made with the term in integrands exponent. And a new term of t2σ2/2 has appeared. Could you be so kind and explain that to me, please...

Can anyone explain intuitively or give a better explanation of multi gaussian beams and the ABCD matrix approach for sound (ultrasonics) and not light? Thanks!

Homework Statement system of equations is as follows 4x +2y -2z = 0 2x + y -z= 1 3x +y -2z = 1 Homework EquationsThe Attempt at a Solution [/B] Using gaussian elimination we can multiply mid-eq, by (-2) [[[actually... it is simply a basic equation procedure]]] 2x+y-z=1 |*(-2) = -4x -2y...

I am trying to evaluate the following integral. ##\displaystyle{\int_{-\infty}^{\infty}f(x,y)\ \exp(-(x^{2}+y^{2})/2\alpha)}\ dx\ dy=1## How do you do the integral above?

I would like to prove that ##\displaystyle{\int dx'\ \frac{1}{\sqrt{AB}}\exp\bigg[i\frac{(x''-x')^{2}}{A}\bigg]\exp\bigg[i\frac{(x'-x)^{2}}{B}\bigg]=\frac{1}{\sqrt{A+B}}\exp\bigg[i\frac{(x''-x)^{2}}{A+B}\bigg]}## Is there an easy way to do this integration that does not involve squaring the...

Consider the partition function ##Z[J]## of the Klein-Gordon theory ##Z[J] =\int \mathcal{D}\phi\ e^{i\int d^{4}x\ [\frac{1}{2}(\partial\phi)^{2}-\frac{1}{2}m^{2}\phi^{2}+J\phi]} =\int \mathcal{D}\phi\ e^{-i\int d^{4}x\ [\frac{1}{2}\phi(\partial^{2}+m^{2})\phi]}\ e^{i\int d^{4}x\...

Usually when gravitational lensing is discussed, the examples are those of matter bending spacetime into a positive curvature. https://commons.wikimedia.org/wiki/File:Gravitational_lens-full.jpg In these cases, distortion of light is clearly evident as images of galaxies from behind these...

Homework Statement What I basically want to do is to prove Gauss Law with a cylinder perpendicular to an infinite charged wire (I know I can do this simple, but I want to do it this way) This is what I have done so far: Homework Equations $$\Phi=\int \frac{dq}{4\pi \varepsilon_0 r^2} \hat{r}...

Homework Statement A thin spherical shell with radius R1 = 2.00 cm is concentric with a larger thin spherical shell with radius 6.00 cm . Both shells are made of insulating material. The smaller shell has charge q1=+6.00nC distributed uniformly over its surface, and the larger shell has charge...

Homework Statement Given the wave function of a particle \Psi(x,0) = \left(\frac{2b}{\pi}\right)^{1/4}e^{-bx^2} , what is the probability of finding the particle between 0 and \Delta x , where \Delta x can be assumed to be infinitesimal. Homework EquationsThe Attempt at a Solution I proceed...

Homework Statement Please help! I'm new to Gaussian and I've been on this problem for hours, I can't crack it at all (no pun intended) can anyone provide a detailed walk through the answers? On average 5% of eggs contain a hereditary condition. Use Gaussian distribution to find the...

Homework Statement I want to evaluate the following definite integral of the form, I = \int\limits_{x = -\infty}^{\infty}\int\limits_{y = -\infty}^{\infty} e^{-ax^2} e^{-by^2} | \cos(c x + d y)| dx dy where a, b, c, and d are constants, as part of a larger problem I am doing, Homework...

Hi all, I think there is a really obvious answer to this, but I just don't see it yet. Suppose you had N data sets that all measured the same quantity as a function of time. Each data set shows the same signal plus a random noise component which is normally distributed about the signal with a...

Hi, I am trying to understand the functional form of B3LYP from the Gaussian output file. I have tried to relate the details in the output file with the functional form of B3LYP. But I am not sure what certain terms correspond to. I have mentioned below the details. Can you pleaese help me. In...

Homework Statement Basically I have to convert from Gaussian Units in a Transmission Line Experiment. I don't get what the point of expressing Capacitance in cm is and I find this very confusing. Homework Equations The equation I've been given is C'=Q'/V=w/4πh, (1) where the prime denotes "per...

Hi, I have a simple/fast question... Can you reliably use a Poisson function to fit on data that seem to be Gaussian distributed (although that is due to the large number of the mean)?

In an image processing paper, it was explained that a 2D Gabor filter is constructed in the Fourier domain using the following formula: $$ H(u,v)=H_R(u,v) + i \cdot H_I(u,v)$$ where HR(u,v) and HI(u,v) are the real and imaginary components, respectively. It also mentions that the real and...

The superposition of a gaussian beam and a plane wave generates a pattern of rings whose phase shift before and after the focal plane (of the gaussian beam) is ##\pi##. This means that if you measure interference before and after you'll see the minimums and maximums of intensity invert. We can...

Hello, I have been I am trying to optimize a molecule (crowded) with the chemical formula C60H52O18P4S4W2. The problem arises after 2 days, which means that the initial geometry was not a problem. " GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad Berny optimization...

Why doesn't the flux through a Gaussian surface change, when the shape is changed? (while keeping the net charge inside it the same) Flux is the dot product of electric field and surface area, so wouldn't it change if surface area is changed?

Hi, I was looking at derivation of a multi gaussian beam to represent the ultrasonic beam from a transducer through a fluid. In the derivation a complex valued symmetrical 2x2 matrix is used whose imaginary part of eigen values is more than zero. Can someone please tell me what are the...

This system can be written as a matrix equation $\displaystyle \begin{align*} A\,\mathbf{x} = \mathbf{b} \end{align*}$ as $\displaystyle \begin{align*} \left[ \begin{matrix} \phantom{-}2 & 4 & \phantom{-}0 & 1 \\ \phantom{-}2 & 8 & -2 & 7 \\ -2 & 2 & -2 & 7 \\ \phantom{-}0 & 8 & -5 & 11...

Probably a stupid question, but I do not get it... Here you can see an experiment demonstrating the Gaussian gun: Here I understand how momentum is conserved, i.e. the smaller mass of the ejected ball times its high speed is equal the bigger total mass of the recoiling masses times its...

I'm not sure where you're getting the idea that z = 2, as this is not correct. I'm assuming this is to be done without pivoting... Set up your augmented matrix: $\displaystyle \begin{align*} \left[ \begin{matrix} 2 & \phantom{-}1 & -3 & -5 \\ 1 & -1 & \phantom{-}2 & 12 \\ 7 & -2 & \phantom{-}...

Please bear with me because I'm only in Pre-calculus and am taking basic high school physics. This is completely outside of my realm but curiosity has taken the better of me. I just learned last week about the difference between Euclidean Geometry and Riemmanian Geometry (from another thread...

Hey, folks. I'm doing a problem wherein I have to evaluate a slight variation of the Gaussian integral for the first time, but I'm not totally sure how to go about it; this is part of an integration by parts problem where the dv is similar to a gaussian integral...

Homework Statement An infinitely long, cylindrical, conducting shell of inner radius b and outer radius c has a total charge Q. A line of uniform charge distribution Λ is placed along the axis of the shell. Using Gauss's Law and justifying each step, determine. A) The Electric Field for r>a...

Hello If we have a gaussian surface that is placed in a uniform electric field E and encloses 0 charge, what would the E-field at the gaussian surface be? I have assumed the gaussian surface to be cubic surface, and then I have found from Gauss's law that the electric field is zero at the...

Homework Statement I started with the following equations : 3w+2x+3y+z=76 w+2x+2y+z=59 w/2+x+y+z/4=21 Homework Equations Gaussian elimination The Attempt at a Solution So I got the following after applying Gauss' method : 3w+2x+3y+z=76 -4x-3y-2z=-101 3/2z=51 which gives z=34 Then I get...

Homework Statement The figure shows a closed Gaussian surface in the shape of a cube of edge length 1.80 m. It lies in a region where the electric field is given by E= (2.86x + 3.82)i + 7.18j + 8.36k N/C, with x in meters. What is the net charge contained by the cube? Homework Equations ε0...

Homework Statement Consider f = wT x, where p(w) ∼ N (w|0, Σ). Show that p(f|x) is Gaussian. The Attempt at a Solution [/B] So there are apparently two approaches to this problem using either the linearity of f in terms of w or moment generating functions. But I'm having a lot of trouble...

Hello everyone, I know this is a very basic question but I was wondering, in the context of inflation, what does it mean to have gaussian or non-gaussian fluctuations. First of all, are we talking about the fluctuations of the inflation? Second of all, how is the nature of the fluctuations...

Say I draw a set of numbers {x1,x2,x3,...} from a normal distribution and apply a function f(x) to these. Will the new set of numbers {f(x1),f(x2),f(x3),...} be gaussianly distributed? I guess it depends on f(x), since for example f(x)=x would certainly mean that the new set is gaussianly...

I am simulating a radio telescope and confused on what kind of source should I setup to simulate a star. Should it be a TEM00 gaussian beam or simply a plane wave?Cheers, Robin

I have a question regarding the relationship between the Biot-Savart formula in Gaussian and Lorentz-Heaviside units. In Gaussian, we have a ##\frac{1}{c}## outside the integral, but in LH units we have a ##\frac{1}{4\pi}\frac{1}{c}##. This does not make sense, considering the transformation...

I heard a guy mention in a debate that some math calculation didn't obey Gaussian statistics. It was a debate re: the economy (not important here, though). I was curious what was meant by "Gaussian statistics" and would appreciate if anyone could offer a sort of layman's definition. Thanks...

Homework Statement Let $$(X(n), n ∈ [1, 2])$$ be a stationary zero-mean Gaussian process with autocorrelation function $$R_X(0) = 1; R_X(+-1) = \rho$$ for a constant ρ ∈ [−1, 1]. Show that for each x ∈ R it holds that $$max_{n∈[1,2]} P(X(n) > x) ≤ P (max_{n∈[1,2]} X(n) > x)$$ Are there any...

Homework Statement I am struggling with one of the end of chapter questions in my QM textbook (see attachment as I don't know how to show calculus on PF). It has thrown me because the chapter introduces some of the key principles in QM by talking about probability but then it randomly chucks in...

A Gaussian beam has an intensity I(r,z), if the beam area at position Z is given by A(Z), then the beam gets focused by a lens of focal length f, what will the area of the beam be at the beam waist A(0) be? So I have been trying to figure this out for ages, I had to replicate an experiment in...

Homework Statement A beam of wavelength 600 nm has initially an intensity profile of Gaussian shape with a fwhm of 1 mm. Determine the intensity profile and fwhm 10 meter away.Homework Equations FWHM = λ/(2NA√(1 + I/Is)) The Attempt at a Solution [/B] FWHM1 = 1mm = 600 nm/(2NA√(1 + I/Is))...

Hi. Has anybody here any experience with SciPy? I'm trying to get SciPy to adjust a gaussian function to some data. For more details its the photopeak of Co60. This is what I do: import numpy as np from scipy.optimize import curve_fit # counts is a numpy array which...

Maybe a picture will help. http://chipreuben.com/annihilation-of-shifted-Gaussian.jpg I get zero, both with the shifted and the non-shifted. Can anyone tell why the nonshifted should yield the ground state eigenfunction multiplied up by a constant? It seems the answer has to do with expanding...

Homework Statement Hello all I apologize for the triviality of this: Im new to this stuff (its easy but unfamiliar) I was wondering if someone could verify this: Find the G.C.D of a= 14+2i and b=21+26i . a,b \in \mathbb{Z} [ i ] - Gaussian Integers Homework Equations None The Attempt...